Posted by **jackie** on Tuesday, December 1, 2009 at 4:47pm.

f(x)= x^2 / (x-2)^2

find the intervals of concavity and the inflections points

- calc -
**bobpursley**, Tuesday, December 1, 2009 at 4:48pm
I will be happy to critique your work.

- calc -
**MathMate**, Tuesday, December 1, 2009 at 5:11pm
If the function is twice differentiable within its domain, inflection points occur at values of c where f"(c)=0.

Note that not all points where f"(c)=0 are inflection points.

You need to check the concavity *between* points where f"(x)=0. It is concave up if f"(x)>0 and concave down if f"(x)<0.

X=c is an inflection point if all of the following conditions are satisfied:

1. f(x) is twice differentiable at c.

2. f"(c)=0

3. f"(c+) has a different sign than f"(c-), i.e. concavity changes.

Now it's time for you to sharpen your pencil and show us some work.

## Answer this Question

## Related Questions

- Calculus - Graph the following function. Find and state the domain, intercepts, ...
- Calculus - f(x)= x/(1+x)^2 a) find the intervals on which f is increasing or ...
- calculus - y=5/x-3 find the zeros,relative min and max.the max and min find the ...
- Calculus - Consider the function f (x) = 2x^3 - 3x^2 - 72x + 7 Find and classify...
- Calculus - Consider f(x)=200+8x^3+x^4. find the intervals on which function is ...
- calculus I - hi! can someone please help me ... question: a)find the intervals ...
- math-calc - Consider the function f(x)= (2x+8)/(6x+3). For this function there ...
- calculus - Please help!! Okay so my teacher has been away and hasent explained ...
- CURVE SKETCHING PLEASE HELP - Okay so my teacher has been away and hasent ...
- calculus - Find the asymptote, interval of monotonicity, critical points, the ...